Cecil Moore wrote:
Gene Fuller wrote:
Let's see some real numbers.

The numbers are trivial. What is important is the concept.
In the experiment, the Pref1 wave disappears between
steady-state #1 and steady-state #2. Here's the question
that you and others have refused to answer.

When an EM wave disappears in its original direction of
travel, what happens to its energy?

OK, but first let's set the ground rules.

The ONLY thing under discussion here is our disagreement about the
canceling waves heading back toward the source from the match point. You
claim those waves must exist and then cancel over a short distance (I
believe you reduced the distance to 'dx' or something similar.) I claim
those waves never exist at all and therefore don't need to be canceled.

If you have anything else in mind, then enjoy your solo activity,
whatever that might be.

So just what "trivial" numbers are required?

First, it is not clear how one make an instant transition from a 50 ohm
environment to a 300 ohm environment. Do you just connect a 50 ohm coax
to a 300 ohm coax? Or do you prefer to connect a 50 ohm twin-lead to a
300 ohm twin-lead? (Good luck with either of these.) If you want to
connect a 50 ohm coax to a 300 ohm twin-lead then you are going to need
some sort of transition device.

Oops! Where is the match point now? Ordinarily we would not really care
very much about such things, but you have stated that important things
are happening within the "dx" zone. It is a safe bet that the Z0
transition is not abrupt either. The "trivial" numbers just got a bit
more complicated.

Let's look at the conservation of energy part. You like to use the
Poynting vector, so we can stick with that. The first thing to note is
that the Poynting vector is E x H, not V x I. Perhaps only a minor bump
in the road, but the transition from E to V and H to I is not quite so
trivial at discontinuities such as the "match point".

But let's muddle ahead in any case. The integral form of the Poynting
theorem goes like the following.

* Define a test volume with a closed surface. There is no particular
size required, although infinite and zero don't work well for practical
reasons.

* Calculate the Poynting vector at all points on the closed surface.

* Integrate the 'normal' component of the Poynting vector over the
entire surface. This integral then represents the net electromagnetic
energy flowing into (or out of) the test volume. I believe this is what
you would consider the energy carried by the waves of interest. Note
that all waves are combined together; they are not treated separately.

* The Poynting theorem says that the net energy flow must be balanced by
the change in electromagnetic energy content within the test volume and
the work done by the fields on any charges within the test volume.

* Note that a change in field strength within the test volume is tied to
the change in electromagnetic energy content. Any charges within the
test volume can be accelerated. Remember, this sort of match point
cannot exist in free space, so there are charges in the region of interest.


This sort of description and the associated derivations can be found in
any ordinary E&M textbook.


You might notice that the Poynting theorem, i.e. conservation of energy
law for EM, says nothing about the sanctity of waves or about the
conservation of energy in waves. It does not say that the integral of
the Poynting vector over the test volume surface must be zero.

Even more importantly for this discussion, the Poynting theorem does not
help at all with your assertion that important things are happening in
the 'dx' zone. If you make the test volume size smaller than your 'dx'
then you run into trouble with the finite size of the transition region
described above. If you make the test volume large enough to contain the
'dx', then all of the purported interesting stuff happens inside. Again,
the Poynting theorem tells nothing.


If you want to believe in the conservation of waves, go right ahead.
Just don't expect conservation of energy to support your case.
Mathematically it cannot.


73,
Gene
W4SZ